I have a RD-4700-GS SHIMANO TIAGRA (Rear Derailleur,Medium Cage,10-speed) and a CS-HG50-10 (SHIMANO DEORE, 10-Speed, 11-36T MTB Cassette Sprocket). However, the RD-4700-GS is compatible with a Low sprocket_Max. of 34T (Front double) 32T (Front triple) as on the shimano website. What issues can I expect if the sprocket teeth ratios are different? And how perhaps can I resolve this incompatibility?
Most likely it'll work assuming you don't exceed the derailleur capacity. Shimano specs components by using perfect shifting as the rule. If you exceed the specifications, usually you'll first have slightly less than perfect (but still good enough) shifting before it ceases to work.
By selecting suitably sized chainrings, you can avoid the cassette gearing causing derailleur capacity problems, but chainrings are so expensive that I'd say if you exceed the capacity it's probably easiest to use the 11-34T cassette for which it is intended. However, in today's market you may not find a cassette of the proper gearing and if you do it's likely to go out of stock tomorrow if you don't buy it already today, and if you buy it, the price will be 50% higher than previously.